Modern diesel engines use variable geometry turbines (VGT) to increase the amount of air supplied to the engine cylinders. The VGT varies the angle of the turbine stator inlet vanes to change the amount of air supplied to the engine cylinders. In addition to providing optimum performance and fuel economy, modern diesel engines must also meet stringent federal regulations on emissions, particularly, particulate matter and nitrogen oxides. In order to meet all of these requirements, diesel engines with a VGT also use an exhaust gas recirculation (EGR) valve that has a variable controlled position to recirculate varying amounts of engine exhaust gases back into the engine cylinders to lower temperature of combustion, reduce NOx production and reduce engine emissions. As the engine operates over a large range of operating conditions, including engine speed, fuel usage, engine load, etc., one and typically multiple controllers are embedded in the engine control unit (ECU) to control various engine actuators in response to sensors detecting engine performance in order to optimize engine performance, and emissions.
An important example of a real-time, embedded optimization problem is model predictive control (MPC), where an optimal control problem over a receding horizon is solved during each sampling period. See L. Grüne and J. Pannek, “Nonlinear model predictive control,” in Nonlinear Model Predictive Control, pp. 43-66, Springer, 2011; J. B. Rawlings and D. Q. Mayne, Model predictive control: Theory and design. Nob Hill Pub., 2009; and G. C. Goodwin, M. M. Seron, and J. A. De Doná, Constrained control and estimation: an optimisation approach. Springer Science & Business Media, 2006, each incorporated herein by reference in their entirety. The optimal control problem for a discrete time linear-quadratic MPC formulation can be expressed as a convex QP. Furthermore, convex QPs form the basis for many algorithms used in nonlinear model predictive control (NMPC) such as sequential quadratic programming (SQP), or the real-time iteration scheme which solves just one QP per timestep. See P. T. Boggs and J. W. Tolle, “Sequential quadratic programming,” Acta numerica, vol. 4, pp. 1-51, 1995; S. Gros, M. Zanon, R. Quirynen, A. Bemporad, and M. Diehl, “From linear to nonlinear mpc: bridging the gap via the real-time iteration,” International Journal of Control, pp. 1-19, 2016; and M. Diehl, H. G. Bock, J. P. Schlöder, R. Findeisen, Z. Nagy, and F. Allgöwer, “Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations,” Journal of Process Control, vol. 12, no. 4, pp. 577-585, 2002, each incorporated herein by reference in their entirety.
The use of Model Predictive Control (MPC) is growing for engine control. For example, the rate-based MPC approach incorporates integral type action to guarantee zero steady state error by adding additional integral states to the predictive control model. The MPC model uses a number of different engine operating ranges (fuel rate and engine speed), and develops a controller for each range to control the engine actuators.
In a specific example of model predictive control applied to diesel engine airflow, the flows in the engine are controlled using the variable geometry turbine (TGT), EGR throttle, and an EGR valve actuator. These systems are strongly coupled and are highly non-linear.
However, existing methods for constrained optimal control in embedded automotive applications have been unable to perform required calculations within a time period necessary for real-time control. In a control system for a diesel engine, the Engine Control Unit (ECU) samples input signals, records measurements from sensors, performs calculations and issues commands. To accomplish real-time control, all of these operations must be performed within the sampling period. In particular, the ECU is given a fixed percentage of the sampling period to complete all required calculations, referred to as a computational budget.
In recent years a significant amount of research into developing fast, reliable algorithms for solving both QPs and more general optimization problems online has significantly advanced the state of the art. However, managing the computational burden of online optimization algorithms remains a challenge.
It would be desirable to provide a model predictive controller for use with internal combustion engine, which is fast enough to accomplish all required calculations within the computational budget.
The foregoing “Background” description is for the purpose of generally presenting the context of the disclosure. Work of the inventors, to the extent it is described in this background section, as well as aspects of the description which may not otherwise qualify as prior art at the time of filing, are neither expressly or impliedly admitted as prior art against the present invention.